Hmmm, I can at least see why they would want to get Singapore. Singapore is a nice trade hub and has English as an official language and acts as a lingua franca in the city, so it would make sense for an "easier" expansion, because at least a lot of them probably still speak English in Fallout-verse, if not a heavily English-based language that has many elements from the other official and recognized languages of Singapore.
Though the actual state of it after the nukes fell is another question.
As for the Philippines, probably because the Philippines in real life has English as an official language so there would be a noticeable amount of people there who speak it even after the bombs fell in Fallout-verse presumably, it would also act as a nice base of operations near Asia so they won't have to worry about basing rights or anything if they actually own the territory it is set up in.
Plus you know, there was the actual
Commonwealth of the Philippines which was under the United States (which is the reason for English being an official language there in real life) until their independence, which the United States can use to justify their annexation by saying they are regaining a "lost commonwealth" as it were. Even if that is really stretching their claims.